12 Dec, 14:42
Prop Cian Healy is expected to miss the start of the 2014 RBS 6 Nations after undergoing surgery on his injured ankle on Wednesday.
Davidson spent four years as Dungannon's coach, taking over from New Zealander Andy Earls and gradually improving the Tyrone side's fortunes - they finished sixth this season in AIB League Division One and also won the Jack Kyle Cup.
A statement from Dungannon read: "Jeremy has been an extremely dedicated and hardworking worker for club rugby and he will be sorely missed at the club.
However, this was too good an opportunity to miss and we have no doubt that he will continue to develop as a coach and prove to be very successful coach at the highest level.
The club is now preparing for the new season and we are considering our options for a new coaching team."
Davidson, a fluent French speaker, spent three seasons playing for Castres and captained the club in 2000 before moving back home to see out his career with Ulster. A knee injury prematurely ended his playing days in 2003.
Commenting on his move back to Castres, Davidson said: "It was an opportunity that I just could not turn down. I loved my time with Castres as a player and I will be returning to link up with head coach Ugo Mola, the former French full-back whom I played alongside.
"However, the move is tempered by my love of Dungannon and the players and backroom staff that I worked with. I have really enjoyed my four years at Stevenson Park where I learned an awful lot about coaching.
"I was able to learn the ropes and utilise my philosophy of the game. Now I feel ready for the next big step," added the 33-year-old, who has signed a preliminary two-year contract with the Stade Pierre-Antoine residents.